In recent diaries we've looked at some pretty advanced, deep stuff. Godel, Cantor, Euclid. Heavy going. Today, fun stuff with really elementary math: Multiplication. Of regular number numbers --- positive integers. But interesting patterns.
This is not only kinda neat, but could also be used by teachers in elementary or junior high....
For more, join me below the fold
I borrow a lot of this from Alfred Possamentier's wonderful Math Charmers. It's a lot of fun.
Let's multiply 1s. That is, numbers made up of just 1s. Like this
1 * 1 = 1
11 * 11 = 121
111 * 111 = 12,321
1,111 * 1,111 = 1,234,321
11,111 * 11,111 = 123,454,321
111,111 * 111,111 = 12,345,654,321
1,111,111 * 1,111,111 = 1,234,567,654,321
11,111,111 * 11,111,111 = 123,456,787,654,321
111,111,111 * 111,111,111 = 12,345,678,987,654,321
Huh......
How about when the two numbers aren't equal?
11 * 111 = 1,221
11* 1111 = 12,221
11*11111 = 122,221 and so on
111 * 1111 = 123,321
111 * 11,111 = 1,233,321 and so on.....
THAT'S NEAT
Can we explain it?
Well.......let's see
Try with 111*111
111
X 111
--------
111
111
111
-------
12321
so, the number of 1's that get added is more in the middle than at the ends, and goes up by 1 each time.